Question

Which statements about this system of equations are true? Check all that apply 2 x minus 7 y = negative 13. Negative 2 x + 11 y = 1. The x-variable will be eliminated when adding the system of equations. The y-variable will be eliminated when adding the system of equations. The sum of the system of equations is 4 y = negative 12. x = 17 y = negative 3 There are infinitely many solutions to the system of equations.

Answer 1

Answer:

1 and 3.

Step-by-step explanation:

The given system of equations

$2x-7y=-13$     ...(1)

$-2x+11y=1$     ... (2)

Here, coefficients of x have same values with opposite signs.

The x-variable will be eliminated when adding the system of equations.

Add (1) and (2), we get

$2x-7y-2x+11y=-13+1$

$4y=-12$

Divide both sides by 4.

$y=-3$

Put y=-3 in (1).

$2x-7(-3)=-13$

$2x+21=-13$

$2x=-13-21$

$2x=-34$

Divide both sides by 2.

$x=-17$

So, the given system of equations have unique solution, i.e., (-17,-3).

Therefore, the correct options are 1 and 3.